For what value 'a' and 'b', the following system of linear equations have an infinite number of solutions?
(2a - 1)x - 3y = 5
3x + (b - 2)y = 3

Asked by tv2000in | 16th Apr, 2017, 11:19: PM

Expert Answer:

begin mathsize 16px style For space infinitely space many space solutions space condition space is comma
straight a subscript 1 over straight a subscript 2 equals straight b subscript 1 over straight b subscript 2 equals straight c subscript 1 over straight c subscript 2
Given space that
open parentheses 2 straight a minus 1 close parentheses straight x minus 3 straight y equals 5
3 straight x plus open parentheses straight b minus 2 close parentheses straight y equals 3
Here comma space
straight a subscript 1 equals 2 straight a minus 1 comma space straight a subscript 2 equals 3
straight b subscript 1 equals 3 comma space straight b subscript 2 equals straight b minus 2
straight c subscript 1 equals 5 comma space straight c subscript 2 equals 3
fraction numerator 2 straight a minus 1 over denominator 3 end fraction equals fraction numerator 3 over denominator straight b minus 2 end fraction equals 5 over 3
Solving space fraction numerator 2 straight a minus 1 over denominator 3 end fraction equals 5 over 3
you space will space get space straight a equals 3
Also comma space solving space fraction numerator 3 over denominator straight b minus 2 end fraction equals 5 over 3
You space will space get space straight b equals 1 fifth

end style

Answered by Sneha shidid | 17th Apr, 2017, 08:19: AM